Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians

We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two-dimensional degeneracy for CuInCr4Se8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8, and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.